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Proceedings Paper

The optimum approximation of a multidimensional filter bank having analysis filters with small nonlinear characteristics
Author(s): Yuichi Kida; Takuro Kida
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Paper Abstract

Firstly, we present the optimum interpolation approximation for multi-dimensional vector signals. The presented approximation shows high performance such that it minimizes various worst-case measures of error of approximation simultaneously. Secondly, we consider a set of restricted multi-dimensional vector signals that all elements of the corresponding generalized spectrum vector are separable-variable functions. For this set of restricted multi-dimensional vector signals, we present the optimum interpolation approximation. Moreover, based on this property, putting the variables to be identical with each other in the approximation, we present a certain optimum interpolation approximation for generalized filter bank with generalized non-linear analysis filters. This approximation also shows the high performance similar to the above-mentioned approximations. Finally, as a practical application of the optimum interpolation approximation for multi-dimensional vector signals, we present a discrete numerical solution of linear partial differential equations with many independent variables.

Paper Details

Date Published: 21 August 2009
PDF: 12 pages
Proc. SPIE 7444, Mathematics for Signal and Information Processing, 744402 (21 August 2009); doi: 10.1117/12.825601
Show Author Affiliations
Yuichi Kida, Ohu Univ. (Japan)
Takuro Kida, Tokyo Institute of Technology (Japan)
Nihon Univ. (Japan)


Published in SPIE Proceedings Vol. 7444:
Mathematics for Signal and Information Processing
Franklin T. Luk; Mark S. Schmalz; Gerhard X. Ritter; Junior Barrera; Jaakko T. Astola, Editor(s)

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